ON ADS-MODULES WITH THE SIP

Mutlu F. T.

BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, vol.41, no.6, pp.1355-1363, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 6
  • Publication Date: 2015
  • Journal Name: BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1355-1363
  • Keywords: Ads-modules, summand intersection property, extending modules, SUMMAND INTERSECTION PROPERTY, INJECTIVE MODULES, RINGS
  • Anadolu University Affiliated: Yes

Abstract

The class of ads modules with the SIP (briefly, SA-modules) is studied. Various conditions for a module to be SA-module are given. It is proved that for a quasi-continuous module M, M is a UC-module if and only if M is an SA-module. Also, it is proved that the direct sum of two SA-modules as R-modules is an SA-module when R is the sum of the annihilators of these modules.